Fuzzy Normal Operator in Fuzzy n-Hilbert Space and Its Consequent Results

الملخص

In this paper, we systematically study the concept of a fuzzy normal operator defined on a fuzzy n-Hilbert space (briefly denoted as space). The work begins with a rigorous presentation of the fundamental definitions related to fuzzy n-inner product spaces and fuzzy n-Hilbert spaces, establishing the necessary theoretical framework for our study. We then formally define fuzzy normal operators within this setting and investigate their structural and algebraic properties. Several key theorems are presented and proved to characterize the behavior of fuzzy normal operators in spaces. In particular, we explore conditions for normality in the fuzzy context, relationships between fuzzy adjoint operators and fuzzy normal operators, as well as important operator-theoretic properties that arise from the interaction between fuzziness and the n-inner product